The problem with flipping the coin is that it already asks you to make an uncomfortable judgement about the values of John and Lisa’s lives. You have already said “Our lives’ values are comparable enough to merit coin-flipping”. Acting out of the view of the partner gives the sort of mutual plausibly deniability that allows you to both percieve that the partner values your more than themselves.
The problem with flipping the coin is that it already asks you to make an uncomfortable judgement about the values of John and Lisa’s lives. You have already said “Our lives’ values are comparable enough to merit coin-flipping”. Acting out of the view of the partner gives the sort of mutual plausibly deniability that allows you to both percieve that the partner values your more than themselves.